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Thread: Compact Sets

  1. #1
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    Compact Sets

    Let S be a subset of the reals. Prove that S is compact iff every infinite subset of S has an accumulation point in S.

    This is what I have so far (which is not much):
    Let S be compact
    Then every infinite subset of S has an accumulation point in S by Bolzano Weierstrass.

    Going the other way is giving me troubles, so any help on that would be much appreciated.
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  2. #2
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    Quote Originally Posted by steph615 View Post
    Going the other way is giving me troubles, so any help on that would be much appreciated.
    Hint: A set is closed if and only if every every convergent sequence in S has its limit in S.
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